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我也给个题目，请高手证明（真或伪）： -- Anonymous - (772 Byte) 2002-3-20 周三, 上午10:45 (398 reads) |
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作者：Anonymous 在 罕见奇谈 发贴, 来自 http://www.hjclub.org
The point is:
Suppose {f_n(x)} is a continous function series which converges to f(x) on [0, 1].
Then:
it's NOT necessarily true that the series
{integral of f_n(x) on [0, 1] } converges to integeral of f(x) on [0, 1].
Mathematically, "convengence in uniform" is a sufficient condition
that's generally satisfied.
Unfortunately, the settings in this problem, as you can check,
does not satisfy it.
In mathematics, this "exchange of limit sign with other operators (integral, derivative, etc.)" cannot be applied arbitrarily. One first has to take the burden
to prove that this exchange is VALID. It's usually a big burden.
作者：Anonymous 在 罕见奇谈 发贴, 来自 http://www.hjclub.org |
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